BOUNDARY-LAYER RESOLVING PSEUDOSPECTRAL METHODS FOR SINGULAR PERTURBATION PROBLEMS

Pseudospectral methods are investigated for singularly perturbed bound ary value problems for ordinary differential equations (ODEs) which po ssess boundary layers. It is well known that if the boundary layer is very small then a very large number of spectral collocation points is required to obtain accurate solutions. We introduce here a new effecti ve procedure based on coordinate stretching and the Chebyshev pseudosp ectral method to resolve the boundary layers. Stable and accurate resu lts are obtained for very thin boundary layers with a fairly small num ber of spectral collocation points.